1. INTRODUCTION Laboratory tests indicate dependence of rock strength on specimen size. In particular, the nominal tensile stress associated with specimen failure decreases in an empirical power-law relationship to specimen size (e.g. [1]). This is usually explained by reasoning that tensile strength is not a true material property but depends on the specimen geometry and probable maximum flaw size that is subjected to tensile loading. Another manifestation of the size effect is expressed in the critical energy release rate associated with fracture extension — fracture energy, for short, which relates to the square of the fracture toughness — increasing usually in an empirical power-law relationship to specimen/notch/intact ligament/crack size (e.g. [2,3]). Although previous experimental works have indicated in most cases a power-law relationship at the laboratory scale ( 1 < m), and have led to a number of theoretical recommendations regarding the treatment of fracture in heterogeneous materials (e.g. [4,5,6,2]), how these results and theories can be appropriately extended to larger scales remains fundamentally unclear. The overarching objective of this work is to develop a new method for estimating how the fracture toughness depends on the size of the fracture that is practically applicable at scales far exceeding laboratory limitations. It is based on hydraulically fracturing rocks at a shallow depth, that is, so that the radius of an initially horizontal, circular fracture attains a value that is several times greater than its initial depth. As these shallow hydraulic fractures grow, the asymmetry of the fracture opening induces curving of the fracture towards the surface so that the geometry resembles a concave-upward saucer. Previous research has shown that the saucer-shapes are, for homogeneous brittle materials such as glass and polymethyl methacrylate (PMMA), determined to leading order by a parameter that compares the in-situ compressive stress acting parallel to the free surface with a fracture toughness dependent estimate of the magnitude of the fracture-induced stress field [7,8,9]. Hence, these prior works show that the final saucer- shape relates directly to the fracture toughness of the material. Therefore, with knowledge of the in-situ stress field, one may in principle estimate the fracture toughness based on a posteriori measurements of the fracture shape and without requiring typically unreliable ARMA 10-237 Deviation from Linear Elastic Fracture in Near-Surface Hydraulic Fracturing Experiments with Rock Makhnenko, R.Y. University of Minnesota, Minneapolis, MN, USA Bunger, A.P. CSIRO Earth Science and Resource Engineering, Clayton, Victoria, Australia Detournay, E. University of Minnesota, Minneapolis, MN, USA Copyright 2010 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 44 th US Rock Mechanics Symposium and 5 th U.S.-Canada Rock Mechanics Symposium, held in Salt Lake City, UT June 27–30, 2010. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The ABSTRACT. This paper presents the results of near-surface hydraulic fracturing experiments in a medium-grained gabbro that make use of different specimen sizes in order to observe the influence of rock heterogeneity and/or non-LEFM behavior on fracture propagation. A comparison of the results with laboratory experiments in brittle elastic materials shows that fracture paths in rock usually do not monotonically approach the free surface. Moreover, they exhibit a high degree of non-symmetry, in contrast to experiments in glass or PMMA. An attempt to correlate crack path variation among different sized specimens to a size dependent fracture toughness has been initially inconclusive due to the noise caused by these crack path complexities. Nonetheless, these results provide an initial demonstration of non-LEFM behavior in hydraulic fracturing with implications for ongoing experiments aimed at quantifying the size effect on rock fracture toughness.
Deviation from Linear Elastic Fracture in Near-Surface Hydraulic Fracturing Experiments with Rock
May 22, 2023
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